This is the second of three lectures on introduction to vertex operator algebras. In this lecture, we shall continue Professor Dong’s lecture to present more fundamental properties of vertex operator algebras. From the mathematical point of view, a vertex operator algebra formally resembles a Lie algebra because the Jacobi identity is used as one of the main axioms. For the Lie algebra aspect o...

The idea that observing an action triggers an automatic and obligatory activation of an imitative action in the motor system of the observer has recently been questioned by studies examining complementary actions. Instead of a tendency for imitation, cooperative settings may facilitate the execution of dissimilar actions, resulting in a relative disadvantage for imitative actions. The present s...

The Drosophila mutants amnesiac, dunce (dnc), and rutabaga were isolated after associative conditioning tests, during which animals were trained to associate the presence of an odor with that of electric shocks (ES). In the absence of conditioning, the odor avoidance (OA) of these mutants was shown to be normal, indicating that their poor associative conditioning performance was attributable to...

The pituitary adenylate cyclase activating polypeptide (PACAP) type I receptor (PAC1) is a G-protein-coupled receptor binding the strongly conserved neuropeptide PACAP with 1000-fold higher affinity than the related peptide vasoactive intestinal peptide. PAC1-mediated signaling has been implicated in neuronal differentiation and synaptic plasticity. To gain further insight into the biological s...

This paper revisits the classical neuroscience paradigm of Hebbian learning. We find that a necessary requirement for effective associative memory learning is that the efficacies of the incoming synapses should be uncorrelated. This requirement is difficult to achieve in a robust manner by Hebbian synaptic learning, since it depends on network level information. Effective learning can yet be ob...

Fear conditioning is a form of associative learning in which subjects come to express defense responses to a neutral conditioned stimulus (CS) that is paired with an aversive unconditioned stimulus (US). Considerable evidence suggests that critical neural changes mediating the CS-US association occur in the lateral nucleus of the amygdala (LA). Further, recent studies show that associative long...

On a hypergroupoid one can define a topology such that the hyperoperationis pseudocontinuous or continuous. In this paper we extend thisconcepts to the fuzzy case. We give a connection between the classical and thefuzzy (pseudo)continuous hyperoperations.

Today power consumption is considered to be one of the important issues. Therefore, its reduction plays a considerable role in developing systems. Previous studies have shown that approximately 50% of total power consumption is used in cache memories. There is a direct relationship between power consumption and replacement quantity made in cache. The less the number of replacements is, the less...

We show that if $R$ is a ring with an arbitrary idempotent $e$ such that $eRe$ and $(1-e)R(1-e)$ are both strongly nil-clean rings‎, ‎then $R/J(R)$ is nil-clean‎. ‎In particular‎, ‎under certain additional circumstances‎, ‎$R$ is also nil-clean‎. ‎These results somewhat improves on achievements due to Diesl in J‎. ‎Algebra (2013) and to Koc{s}an-Wang-Zhou in J‎. ‎Pure Appl‎. ‎Algebra (2016)‎. ‎...

Let R be an associative ring with identity, C(R) be the category of com-plexes of R-modules and Flat(C(R)) be the class of all at complexes of R-modules. We show that the at cotorsion theory (Flat(C(R)); Flat(C(R))−)have enough injectives in C(R). As an application, we prove that for each atcomplex F and each complex Y of R-modules, Exti (F,X)= 0, whenever Ris n-perfect and i > n.